> what is the upside of working with JSON in SQL over having your app construct and parse JSON objects, but storing the data in a database using more primitive types? 

You use map-like structures (JSON/HStore, etc) for semi-structured user data that you CAN'T define/know a rigid schema for, ahead-of-time.

Think usescases like: Allowing users to write configuration rules, or lists of custom tag <-> value pairs for (whatever), things of these sorts